(A bus operates betweeen the airport and the city center. A taxi costs 40 Lei.)
There are five daily trains to/from Brasov, (6.5-9 hours), two to/from Bucharest (9.5-10 hours), and one to/from Timisoara (6.5 hours). There is also a daily train to/from Budapest. Service to Cluj-Napoca (4 hours) is available with a transfer and 1-hour layover.
A bus is by far the cheapest option to get around. A ticket costs 1.8 lei and can be purchased on board from either the driver or an attendant who is usually sitting elsewhere on the bus. It is an honor system so if you're caught without a ticket or proper ID, you have to pay a fine. The route is posted on the front window of the bus.
Taxis are cheap. Different companies charge slightly different rates. The average per km rate is about 1.68 lei. The cab drivers can speak Romanian and usually Hungarian. Many are also fluent in English.
Rent A Car
Publirent, inchirieri masini la preturi abordabile, livrare prompta, +40 (743) 526 653; Rent a car
321 rentacar, rent a car in Tg. Mures and Cluj, Rent A Car
At the football stadium, you can rent a bike for free for two hours, but you have to sign a contract in Romanian and submit your photo ID.
Targu Mures Fortress, (right in the center of the city). It was built in the 17th century.
Cultural Palace, (center of the city). It is a remarkable building built between 1911-1913 in the Hungarian Art Nouveau style.
The main shopping area is the Trandafirilor Square which is the center of the city.
There are also shopping malls:
Mures Mall, near the city center. The Mall has 5 floors, each of them hosting renowned brands and names, some of them for the first time in Romania.
Promenada Mall, is near the industrial park, on the outskirts of the city. 
Tempo, Morii St. A restaurant with a vast array of dishes and specialties. A lot of character as well with a Hungarian musical band every night.
La Teo Restaurant, Alexandru Papiu Ilarian Nr.1 (right next the Medieval Fortress), ☎ 0265212244, . 11AM-midnight. International dishes and local food. Great coffee, winebar, and house made cakes and deserts. Runed by a friendly owner, Teo.
Whats up, Calarasilor str (At the end of the main strip (coming from the Mall) turn left on the far side of the road. You should see the sign on the road and then its through the arch down the stairs). This small bar gives a cave style feel and is clean and well organized. Decent range of beer, liquors, coffee, tea, and the popular hot chocolate drinks in various flavors.Whisky or cognac: 10-25 lei.
Dublin Irish Pub, Mihai Viteazul Str. An Irish-themed pub that serves Guinness and many other drinks! There is a decent menu of both Irish and other dishes as well. A little on the expensive side.
Being a university town, there are plenty of clubs to go out at night to have fun with local and international students. smoking is allowed in the clubs, but Jazz has a non-smoking section.